Already serving up to 30 years in the Vermont prison system for the 1999 death of his son, Hann's murder trial began Monday in the 2001 killing of his daughter, Montana, who prosecutors say died in Desert Hot Springs, Calif. She was 2½ months old.

Riverside County prosecutors are pursuing the death penalty for Hann by invoking the "special circumstance" of a previous murder conviction. If the jury finds him guilty of first-degree murder with the special circumstance, it will then decide if the death sentence should be imposed. The other option would be life without possibility of parole.

Hann, who has pleaded not guilty to the first-degree murder charge, has had severe bipolar disorder since early childhood, his lawyer Brenda Miller said. She asked the jury of nine women and three men at Larson Justice Center in California to consider a second-degree murder charge in light of that information.

Miller compared Hann's cycles of rage to a swing on a children's playground - going up and down - and said 10-week-old Montana took the brunt of it one day almost 13 years ago.

"Just as his anxiety and his rage was reaching its peak, Montana began to cry, and her cries got louder and louder, and his rage just exploded," Miller said, at which point Hann punched the baby with a closed fist.

Hann had been treated several times for bipolar disorder, but he checked himself out of facilities against medical advice and refused to take medication.

"Mental illness is no excuse" for what Hann did, Miller said, but she asked the jury to consider the lesser conviction, which carries a sentence of 15 years to life.

Investigators in Arkansas, where Montana's remains were found, determined she died while her parents lived in Desert Hot Springs, and her body was wrapped inside garbage bags and placed in a "blue Tupperware-type container," deputy Riverside County district attorney Lisa DiMaria said. Then the couple, who DiMaria said lived a "transient, gypsy-style life" beginning in 1998, left for Arkansas. They rented a storage locker, where they kept a trailer containing Montana's body. A year after Montana died, her parents had stopped paying for the locker and the contents were auctioned off. The buyer called police after finding the body.

An all-points-bulletin found Hann and the children's mother, Krissy Lynn Werntz, in a Motel 6 in Portland, Maine, with a 1-month old son, named Jason, who was found to have numerous broken ribs, bleeding under his skull and other internal injuries, according to the prosecution. The state placed this child with foster parents, who eventually adopted him.

Witness Jennifer Bloom, an employee of Maine's Department of Human Services, testified she and a colleague were sent to check on the new baby's welfare, and Hann admitted to being involved with the deaths of his two other children.

"He said he was responsible for both deaths. He didn't provide a lot of detail. He said, 'I fell and blacked out with the baby,'" Bloom said. She added Hann said he felt guilty about the deaths, and felt he had to keep moving to evade police.

The body of the couple's first child, who also was named Jason, was found similarly wrapped in trash bags inside a rubber container, in a storage locker in Lake Havasu City, Ariz. He was 6 weeks old when he died.

Hann was extradited to California in 2009 to be tried for Montana's death, and it took four years for the death-penalty case to make its way through the system and into opening arguments.

DiMaria explained to the jury the two boys would be referred to as "Jason One" and "Jason Two" during the course of the trial to differentiate between them, though the surviving boy also may be called by his adoptive name, Michael.

Almost all witnesses are being flown in from out of state, due to the couple's frequent relocations.

Testimony is expected to end next week.

Werntz, Montana's mother, is facing a murder charge and was originally scheduled to be tried at the same time as Hann, but family medical problems have postponed her trial, DiMaria said.